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We present gravitational waveforms for the last orbits and merger ofblack-hole-binary (BBH) systems along two branches of the BBH parameter space:equal-mass binaries with equal non-precessing spins, and nonspinningunequal-mass binaries. The waveforms are calculated from numerical solutions ofEinstein's equations for black-hole binaries that complete between six and tenorbits before merger. Along the equal-mass spinning branch, the spin parameterof each BH is $\chi_i = S_i/M_i^2 \in [-0.85,0.85]$, and along the unequal-massbranch the mass ratio is $q =M_2/M_1 \in [1,4]$. We discuss the construction oflow-eccentricity puncture initial data for these cases, the properties of thefinal merged BH, and compare the last 8-10 GW cycles up to $M\omega = 0.1$ withthe phase and amplitude predicted by standard post-Newtonian (PN) approximants.As in previous studies, we find that the phase from the 3.5PN TaylorT4approximant is most accurate for nonspinning binaries. For equal-mass spinningbinaries the 3.5PN TaylorT1 approximant (including spin terms up to only 2.5PNorder) gives the most robust performance, but it is possible to treat TaylorT4in such a way that it gives the best accuracy for spins $\chi_i > -0.75$. Whenhigh-order amplitude corrections are included, the PN amplitude of the$(\ell=2,m=\pm2)$ modes is larger than the NR amplitude by between 2-4%.

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Simulations of black-hole binaries with unequal masses or non-precessing  spins: accuracy, physical properties, and comparison with post-Newtonian  results